It's really a matter of how much space you have available. Splitting the bird entirely gives you a little more flexibility in how you arrange things. It doesn't directly impact the outcome, but being able to situate the halves and move them around independently might.
For a couple of years (when I had my COS), I tried spatchcocking, but ended up removing the leg quarters and cooking them separate from the breast. This allowed me to put the dark meat on first (since it would take a little longer), so the breast didn't overcook. Since getting my WSM, I've cooked 'em whole & uncut because there just isn't room to lay out a spatched bird on an 18.5. This year, though, I'm going the twisted turkey route with the rotisserie.
I like the idea of halves this way you can experiment with different rubs, brine's or compound butters.
And if you have a WSM you could hang em with meat hooks.